The Discouragement Effect

Suppose you and I are playing a series of squash matches and we are playing best 2 out of 3. If I win the first match I have an advantage for two reasons. First is the obvious direct reason that I am only one match short of wrapping up the series while you need to win the next two. Second is the more subtle strategic reason, the discouragement effect. If I fight hard to win the next match my reward is that my job is done for the day, I can rest and of course bask in the glow of victory. As for you, your effort to win the second match is rewarded by even more hard work to do in the third match.

Because you are behind, you have less incentive than me to win the second match and so you are not going to fight as hard to win it. This is the discouragement effect. Many people are skeptical that it has any measurable effect on real competition. Well I found a new paper that demonstrates an interesting new empirical implication that could be used to test it.

Go back to our squash match and now lets suppose instead that it’s a team competition. We have three players on our teams and we will match them up according to strength and play a best two out of three team competition. Same competition as before but now each subsequent game is played by a different pair of players.

A new paper by Fu, Lu, and Pan called “Team Contests With Multiple Pairwise Battles” analyzes this kind of competition and shows that they exhibit no discouragement effect. The intuition is straightforward: if I win the second match, the additional effort that would have to be spent to win the third match will be spent not by me, but by my teammate. I internalize the benefits of winning because it increases the chance that my team wins the overall series but I do not internalize the costs of my teammate’s effort in the third match. This negative externality is actually good for team incentives.

The implied empirical prediction is the following. Comparing individual matches versus team matches, the probability of a comeback victory conditional on losing the first match will be larger in the team competition. A second prediction is about the very first match. Without the discouragement effect, the benefit from winning the first match is smaller. So there will be less effort in the first match in the team versus individual competition.

4 comments

Seems like there is a countervailing force: I (the loser of the first game) have to win the 2nd game to have any chance of winning overall; you (the winner of the first game) can save effort in the 2nd game and hope to win by good luck, because you still have the 3rd game as a fall back if you lose.

You could also think of it is giving feedback on my relative ability that then gives me hints on my return to effort (see this paper http://personal.lse.ac.uk/LARCINES/feedback.pdf by bandiera, lacrinese, and rasul in another context)
If this was the story you should see bigger effects when you get new match ups rather than people who had played against each other many times before.

Late to this game… But if you have the same players in each game, the fact that someone lost the first match increases the chances that the winning player has more skill and is more likely to win. If you bring a new pair of players for the second game.. You have a random chance that the losing team now has the better player.

Maybe a setup where the same pair plays the first two games but a new pair plays the third game… Although if one of the original players has a belief that his teammate is inferior or superior, this would affect effort expended.

I agree with “Anonymous”: Testing this will be difficult since the winner of the first contest is, on average, simply a better player. Unless you can credibly account for this difference, I am not sure I would believe any results.

Actually, I think the solution is to have one pair play the first game, and a different pair play the next two. In other words, randomly pair people, but one player wins if he wins the first game, while the other wins only if he wins both. I think this would be the simplest test.